FWIW, I was exactly like this all the way through school. Came up at every parent's evening until age 18. I was very, very shy. My parents didn't socialise a whole lot and I didn't have any pre-school education or many extra-curricular activities away from my family. I went to Brownies but my Mum helped out there so I had no chance to be "me"!
I still managed to land a place at university (Oxbridge) and there, in an education system that had smaller classes and 1:1 tutorials, my confidence grew and I went on to have a successful career pre-DCs.
I still don't like talking on the phone or making phone calls, but I am now reasonably confident. In this day and age, introverts like me can be successful in careers due to email and the internet, it doesn't have to all be about speaking up. As your DD progresses through school her written work will become more important and "speaking up" less-so.
That said, I do think that lack of confidence probably stopped me from taking all the opportunities open to me up to about age 20.
For my DCs, I am determined that they will be more confident, and I do think that confidence (not cockiness) is more important than intelligence with regard to conventional career-based "success". DH has confidence by the bucketload, but not as good an education as me, and through having confidence to take risks with his career and build networks has ended up earning way more than I ever did.
For our DCs, we're trying to ensure they get a variety of social interaction, not just with us, and will be encouraged to take up opportunities as they arise.